Prime divisors in Beatty sequences

William D. Banks*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ⌊ α n + β ⌋, n = 1, 2, ..., where α, β ∈ R, and α > 0 is irrational. For example, we show thatunder(∑, n ≤ N) ω (⌊ α n + β ⌋) ∼ N log log N and under(∑, n ≤ N) (- 1)Ω (⌊ α n + β ⌋) = o (N), where Ω (k) and ω (k) denote the number of prime divisors of an integer k ≠ 0 counted with and without multiplicities, respectively.

Original languageEnglish
Pages (from-to)413-425
Number of pages13
JournalJournal of Number Theory
Volume123
Issue number2
DOIs
Publication statusPublished - Apr 2007

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